Question: Solve for $x$ and $y$ using elimination. $\begin{align*}6x+8y &= 4 \\ 4x-8y &= 6\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $10x = 10$ Divide both sides by $10$ and reduce as necessary. $x = 1$ Substitute $1$ for $x$ in the top equation. $6( 1)+8y = 4$ $6+8y = 4$ $8y = -2$ $y = -\dfrac{1}{4}$ The solution is $\enspace x = 1, \enspace y = -\dfrac{1}{4}$.